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Two-Dimensional Sampling-Recovery Algorithm of a Realization of Gaussian Processes on the Input and Output of Linear Systems

Departamento Telecomunicaciones, Sección de Posgrado e Investigación, Instituto Politécnico Nacional, Unidad Zacatenco, National Polytechnic Institute of Mexico, Ave. IPN s/n, Building Z, Access 4, 3th Floor, SEPI Telecommunications, Mexico City 07738, Mexico
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Entropy 2020, 22(10), 1079; https://doi.org/10.3390/e22101079
Received: 25 August 2020 / Revised: 11 September 2020 / Accepted: 16 September 2020 / Published: 25 September 2020
(This article belongs to the Section Information Theory, Probability and Statistics)
Based on the application of the conditional mean rule, a sampling-recovery algorithm is studied for a Gaussian two-dimensional process. The components of such a process are the input and output processes of an arbitrary linear system, which are characterized by their statistical relationships. Realizations are sampled in both processes, and the number and location of samples in the general case are arbitrary for each component. As a result, general expressions are found that determine the optimal structure of the recovery devices, as well as evaluate the quality of recovery of each component of the two-dimensional process. The main feature of the obtained algorithm is that the realizations of both components or one of them is recovered based on two sets of samples related to the input and output processes. This means that the recovery involves not only its own samples of the restored realization, but also the samples of the realization of another component, statistically related to the first one. This type of general algorithm is characterized by a significantly improved recovery quality, as evidenced by the results of six non-trivial examples with different versions of the algorithms. The research method used and the proposed general algorithm for the reconstruction of multidimensional Gaussian processes have not been discussed in the literature. View Full-Text
Keywords: sampling recovery algorithm of a realization of multidimensional gaussian process; conditional mean rule; basic function; error recovery function; covariance function; cross-covariance function sampling recovery algorithm of a realization of multidimensional gaussian process; conditional mean rule; basic function; error recovery function; covariance function; cross-covariance function
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MDPI and ACS Style

Kazakov, V.; Enciso, M.A.; Mendoza, F. Two-Dimensional Sampling-Recovery Algorithm of a Realization of Gaussian Processes on the Input and Output of Linear Systems. Entropy 2020, 22, 1079. https://doi.org/10.3390/e22101079

AMA Style

Kazakov V, Enciso MA, Mendoza F. Two-Dimensional Sampling-Recovery Algorithm of a Realization of Gaussian Processes on the Input and Output of Linear Systems. Entropy. 2020; 22(10):1079. https://doi.org/10.3390/e22101079

Chicago/Turabian Style

Kazakov, Vladimir, Mauro A. Enciso, and Francisco Mendoza. 2020. "Two-Dimensional Sampling-Recovery Algorithm of a Realization of Gaussian Processes on the Input and Output of Linear Systems" Entropy 22, no. 10: 1079. https://doi.org/10.3390/e22101079

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